# Properties

 Label 2850.103 Modulus $2850$ Conductor $475$ Order $60$ Real no Primitive no Minimal yes Parity even

# Related objects

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter

sage: H = DirichletGroup(2850, base_ring=CyclotomicField(60))

sage: M = H._module

sage: chi = DirichletCharacter(H, M([0,21,10]))

pari: [g,chi] = znchar(Mod(103,2850))

## Basic properties

 Modulus: $$2850$$ Conductor: $$475$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$60$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: no, induced from $$\chi_{475}(103,\cdot)$$ sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 Minimal: yes Parity: even sage: chi.is_odd()  pari: zncharisodd(g,chi)

## Galois orbit 2850.cg

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Related number fields

 Field of values: $$\Q(\zeta_{60})$$ Fixed field: Number field defined by a degree 60 polynomial

## Values on generators

$$(1901,1027,1351)$$ → $$(1,e\left(\frac{7}{20}\right),e\left(\frac{1}{6}\right))$$

## Values

 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$23$$ $$29$$ $$31$$ $$37$$ $$41$$ $$43$$ $$1$$ $$1$$ $$-i$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{12}\right)$$
 value at e.g. 2